(no subject)

[sigmaleph]

The first proof of the irrationality of pi is from 1761 (due to Johann Heinrich Lambert). Here's what I'm curious about: did people think it might be irrational before that?

There's a long history of people trying to approximate pi, first with geometric methods and then with infinite series, and by the time of Lambert's proof the best one had over a hundred decimal places. What did the people doing those calculations think? The concept of irrational numbers was known for a while. Did they think there was a specific fraction they were approximating, had they guessed it might be irrational, did they just not have an opinion on the matter?

Wikipedia claims Euler had conjectured pi was irrational before Lambert's proof. Euler and Lambert were contemporaries; was he the first one to suggest it? Was there a debate on the subject among mathematicians?

(Wikipedia also suggests that the Indian mathematician Aryabhata might have conjectured it circa 500 BC, but the argument given seems pretty thin and even if so I'm more interested in whether it was a widely-held idea among some mathematical community than about whether some specific person thought so)